Question

A steel wire has a cross sectional area of 1.5 x 10^-4 cm^2 and a length of 10.0 m. By how much will it stretch if a 25 kg weight is hung from it? Please answer in millimeters.

Answer 1

Answer: The steel wire will stretch up to 1837.5 mm

Explanation:

We are given:

Mass = 25 kg

Length of wire = 10 m

Area of cross-section of wire = $1.5\times 10^{-4}cm^2=1.5\times 10^{-8}m^2$    (Conversion factor:  $1cm^2=10^{-4}m^2$ )

To calculate the change in stretching, we use the equation:

$E=\frac{Fl}{A\Delta l}$

where,

E = young modulus of steel = $20\times 10^{10}Pa$

F = force exerted by the weight = m g = $25kg\times 9.8m/s^2$

l = length of wire = 10 m

A = area of cross section = $1.5\times 10^{-8}m^2$

$\Delta l$ = change in length = ?

Putting values in above equation, we get:

$20\times 10^{10}=\frac{25\times 9.8\times 10}{1.5\times 10^{-8}\times \Delta l}\\\\\Delta l=1.8375m$

Converting above value in mili meters, we use the conversion factor:

1 m = 1000 mm

So, 1.8375 m = 1837.5 mm

Hence, the steel wire will stretch up to 1837.5 mm